Please show your work.

Common (or Useful) Information :

1. The excitation potential of H is 13.6 eV.
2. The density of states of hydrogen is g_n ~ 2n².

We have been studying the Boltzmann and Saha equations, especially as the pertain to stellar atmospheres. The next set of questions will provide several examples of how to use the equations in practice. (30 pts) A. Find the temperature at which the number density of H atoms in the fundamental state {n=1) are equal to the of its first excited state (Le. the Blamer series) (10 pts) B. How does this temperature compare to where the Balmer lines are maximized in terms of line strength? Does it match? If so explain why or why not? (5pts) C. Assuming that atmosphere of a star is pure H gas with an electron density is 2 x 1015 cm'3, and the partition function of H\" is 1 while the partition function of H| is 2, compute the fraction of neutral H atoms in the gas (hint: this is not ann\" but nltotal) where the temperature is equal to 12,000 K. (15 pts)